Re: "They Use ∂ Differently in Math and Physics. Which is Better?"

(Sorry for finding myself in a mailer that makes it hard not to top-post.)

This an aside about GELLMU, where there is a \newcommand variant \mathsym, taking two arguments and an optional third argument, i.e., with usage

        \mathsym{ symbol-name }{ symbol-rendering }[symbol-meta-info ]

So, in this case, as a very simple example,

         \mathsym{\bdy}{\partial} ,

might be used to flag "boundary" usage of the character ∂.  For more information see section 6.4 of the GELLMU Manual, e.g., https://www.albany.edu/~hammond/gellmu/glman/glman.html#SU-6.4


The optional third argument is for the future -- whatever meta information might be handled in HTML (with MathML) output by (1) web browsers or (2) computer algebra systems (in the case where HTML clips are pasted from a browser).  Needless to say, the GELLMU Project, as it is, contains no non-trivial code for dealing with the optional third argument.  What kinds of meta-information might you want?

It would be up to authors to supply the meta information and up to you (well, the MathML spec) to indicate what meta information should be passed, and how it should be passed, in HTML/MathML output.

        – Bill

________________________________
From: Deyan Ginev <deyan.ginev@gmail.com>
Sent: Thursday, June 20, 2024 7:21 AM
To: Abbas Jaffary <abbas.jaffary2@gmail.com>
Cc: www-math@w3.org <www-math@w3.org>
Subject: Re: "They Use ∂ Differently in Math and Physics. Which is Better?"

Hi Abbas, all,

Interesting additions, thank you.

For k-forms, since those are "differential forms", I wonder if the use already fits in the conventions described in the video.

I see you are referring to overloading the notational use of "∂" with the boundary example in homology.
I wasn't familiar with it until now, wikipedia has a nice overview here:
https://en.wikipedia.org/wiki/Homology_(mathematics)#Construction_of_homology_groups

Different "named concept" uses of ∂ would be relevant additions for the Intent Open list, especially in cases where - quoting you - "it would be nice to say boundary". That is useful for accessibility.

The original youtube video is closer to the OpenMath questions, as it reveals how an operator with the appearance of full formalization - "partial derivative" - may represent (at least) two different formal definitions.
In OpenMath terms, one could have cast the video exposition as two symbols "convention-m:partial-derivative" and "convention-p:partial-derivative".

But I doubt generator tools can realistically infer these without some very purposeful additional help from authors - such as a brand new notational convention.

Deyan


On Thu, Jun 20, 2024 at 8:56 AM Abbas Jaffary <abbas.jaffary2@gmail.com<mailto:abbas.jaffary2@gmail.com>> wrote:
Very interesting!  There is also the differential geometry use of derivatives as one-forms (and k-forms), and the as boundary operator in algebraic topology. In homology, for example, one could likely infer "partial x" as the "boundary of x", though it would be nice to have it say "boundary".

I imagine there will be some crowdsourced effort to accommodate the most popular use cases for fundamental symbols.  Not sure where OpenMath is with this?

On Wed, Jun 19, 2024 at 8:49 AM Deyan Ginev <deyan.ginev@gmail.com<mailto:deyan.ginev@gmail.com>> wrote:
Hello everyone,

I stumbled on a very well-made exposition video, which covers a subtlety in the meaning of  "partial derivative" between mathematics and physics:

https://youtu.be/QFHSHhpbo00


Aside: This topic is not directly related to current conversations about derivative syntax for "intent".

Instead, the presenter has some well-reasoned general discussion, a community proposal for adding yet-another notation, and showcases some of the problems that our generator tools also face when trying to infer Content MathML expressions from human-authored math syntax.

Greetings,
Deyan